题目

数学-化简求值难题
(1)化简求值:(X+2/X^2-2X - X-1/X^2-4X+4) ÷ X^2-16/X^2+4X,其中X=2+根号2.
(2)化简求值:(3X/X+2 - X/X-2)+ 2X/X^2-4.其中X=4-根号5.

提问时间：2021-03-15

答案

(1)化简求值:(X+2/X^2-2X - X-1/X^2-4X+4) ÷ X^2-16/X^2+4X,其中X=2+根号2.
(X+2/X^2-2X - X-1/X^2-4X+4) ÷ X^2-16/X^2+4X
=(x^2-4-x^2+x)/x(x-2)^2*x(x+4)/(x+4)(x-4)
=(x-4)/x(x-2)^2*x(x+4)/(x+4)(x-4)
=1/(x-2)^2
=1/2
(2)化简求值:(3X/X+2 - X/X-2)+ 2X/X^2-4.其中X=4-根号5.
(3X/X+2 - X/X-2)+ 2X/X^2-4
=(3x^2-6x-x^2-2x)/(x^2-4)+(2x)/(x^2-4)
=2(x^2-3x)/(x^2-4)